It's the character of Cpl. Max Klinger. He wasn't really a crossdresser; he was just trying to get an early discharge on the grounds for bizarre behavior.
But despite all his efforts, his commanding officers are never fooled, and Klinger is continually frustrated. He later gives up his discharge attempts and is promoted from the rank of corporal to sergeant during the course of the TV series.
Cpl. Max Klinger is played by actor Jamie Farr. He was one of two cast members of the original M✶A✶S✶H (1972) television cast to have actually served in the armed forces in Korea; Farr's tour of duty came in the years after the war. Alan Alda served a six month tour as a gunnery officer in Korea. In addition, the dog tags Farr wore on the M✶A✶S✶H (1972) set were actually his issued set from his time in the Army.
Tip! View Jamie Farr's filmography on IMDb.